A method for macroeconomic consistency in current and constant prices

WORKING PAPERS

and Growth

Country Economics Department The World Bank

December 1989 WPS306

A

Method

for Macroeconomic

Consistency

in Current and Constant

Prices

Ali Khadr

and

Klaus Schmidt-Hebbel

An accounting method for showing budget flow and stock

relations, in current and constant prices, for a six-sector

econ-omy.

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Mareconomic Adjustment and GrowthI

Khadr and Schmidt-Hebbel extend earlier work real holdings and (b) capital gains and losses due on cunent-price budget identities to treat con- to inflation and exchange rate depreciation. This

stant-price flow relations. makes possible a distinction between savin.'

and a changr, in real wealth, or "adjusted" This introduces relative prices and constant- savings.

price values for all relevant output and aggregate

demand components and permits a distinction In Working Paper 310, Khadr and Schmidt-between real variables and relative price Hebbel apply the framework to data on

Zim-changes. babwe for 1981 and 1987.

It also permits breaking the changes in asset and liability holdings down into (a) changes in

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Page

1. INTRODUCTION ... 1

2. A METHODOLOGY FOR MACROECONOMIC CONSISTENCY ... 2

2.1 Flow Budget Constraints in Current Prices ... ... 2

2.2 Flow Budget Constraints in Constant Prices ... ... 9

2.3 Balance Sheets, Net Wealth and Savings ... 28

2.4 Intertemporal Budget Constraints ... 36

2.5 Implications of Macroeconomic Consistency for Macro Analysis and Model Building ... 39

3. APPLICATION TO ZIMBABWE ... 40

3.1 Macroeconomic and Financial Flows in Current Prices .... ... 41

3.2 Macroeconomic and Financial Flows in Constant Prices ... 42

3.3 Balance Sheets and Real Wealth ... 50

4. CONCLUDING REMARKS . ... 54

REFERENCES.55 R FER N E ... .. . . . .. 5

APPENDIX 1 .56

This paper has benefited from many useful comments by Vittorio Corbo, William

Easterly, John Holsen, Gary Hyde, Jacques Polak, Michael Walton and participants at the World Bank Seminar on Macroeconomic Adjustment and Growth, Annapolis, April 24-26, 1989. Efficient research assistance provided by Perla Aizenman and Anna Muganda is gratefully acknowledged.

Macroeconomic consistency can be understood in different ways. At the

simplest level, consistency refers to the satisfaction of within-period and/or

intertemporal budget constraints. Macroeconomic consistency is this sense can

be viewed as the set of restrictions imr-osed by the simultaneous satisfaction

of budget constraints for all sectcrs of the economy. A wider meaning of

macroeconomic consistency pertains to the restrictions that result from both

budgetary rel&tions and behavioral structures. General equilibrium macroeconomic

models which explicitly combine behavioral and accounting relations are

consistent in this second sense.

This paper develops a framework for macroeconomic consistency in the first

sense. It provides an accoutnting model for nominal and real budgetary flow and

stock relations for any economy with reasonable data availability. An

application to Zimbabwe illustrates the scope and the usefulness of the

methodology.

A consistent macroeconomic accounting framework is required for both

financial programming (which often involves few or no behavioral equations) and

for any model-building effort that involves additional structure and behavior.

Since it lacks any behavioral structure, the framework constitutes a minimum

accounting skeleton that integrates the traditional national income, fiscal,

monetary, and balance of payments accounts into a basic grid provided by

source-and-use-of-fund tables or budget constraints for an appropriate number of

sectors.

The consistency model is derived in section 2. The integration of current

price flow budget constraints for six sectors in subsection 2.1 is based on

preceding wo;k on nominal budget flows by United Nations (1968), Turnovsky

and Easterly (1989).

The framntwork is extended significantly in subsection 2.2 to integrate

real national income variables with other budgetary variables using a common

deflator. This procedure implies distinguishing, on the expenditure side,

between real aggregate demand components and relative price changes, and on the

financing side between changes in real asset/liability holdings and capital

gains and losses stemming from inflation and exchange rate devaluation.

Balance sheets and net wealth definitions, based on previous work by Crouch

(1972), Meyer (1975), Turnovsky (1977) and Marshall and Schmidt-Hebbel (1988).

are presented in subsection 2.3. These are a prerequisite for stock or

intertemporal. budget constraints derived subsequently (subsection 2.4), which

necessarily involve current expectations of future flow variables. A discussion

of the implications of macroeconomic consistency for model building concludes

this section.

An application of the consistency framework to the Zimbabwean economy for

1981 and 1987 is presented in section 3. This is a simplified three-sector

version of a six-sector application to Zimbabwe presented by Khadr and

Schmidt-Hebbel (1989). Section 4 concludes.

2. A METHODOLOGY FOR MACROECONOMIC CONSISTENCY

2.1 Flow Budget Constraints in Current Prices

In the following, the flow budget constraints for the main sectors of the

The sectors considered here are two non-financial public sectorr (central

government, and a consolidated public enterprise and local government sector),

two financial sectors (the central bank and the banking sector), the

non-financial private sector, and the foreign sector.

Sector disaggregation is based on factor ownership and sector behavior.

This leads naturally to a distinction among the private, public, and external

sectors. In addition the financial and non-financial sectors are separated due

to the importance of financial and monetary variables in the economy as well as

their relation to balance of payments variables.

The distinction within the public sector is justified on grounds of data

availability (and possibly differing behavior) for the central government budget

in comparison to public enterprises and local government, which are lumped into

a single account. A distinction between deposit money banks and the central

bank is desirable due to their different roles and links with the balance of

payments and the public sector. Obviously they can be easily consolidated into

a single monetary system. Alternatively the central bank, central government,

and public enterprises and local government can be integrated, as in section 3

below, into a consolidated public sector, which often is the relevant aggregation

for analyzing the macroeconomic impact of the public sector on the main

macroeconomic aggregates.1

The private sector consolidates households and firms into one sector, an

assumption which can be lifted subject to data availability and analytical

lFor a detailed derivation of the consolidated public sector budget based

on four public subsectors (general government, public enterprises, central bank,

requirements. Section 3 consolidates the private and banking sectors into one

financial/non-financial private sector.

The two accounting principles for recording transaction flows are the cash

basis and the accruals basis.2 Balance of payments, national income, and

monetary statistics are normally on an accruals basis, while government

statistics are recorded on a cash basis.3 For consistency, the budget

constraints developed below, which integrate data from the above-mentioned four

sources, assume a common accounting principle, the accruals basis.

An imporLant category of accrued but unrealized flows are capital gains

and losses on liabilities and assets. While unrealized capital gains and losses

are not considered in the flow budget constraints, the real flow budget

constraints in section 2.2 below decompose deflated changes in nominal asset and

liability holdings into the sum of changes in real holdings and the capital

gains and losses due to inflation and exchange rate devaluation. By contrast,

real balance sheet accounts in section 2.3 only consider the changes in the

stocks of real assets and liabilities, hence implicitly subtracting the capital

gains and losses from the real changes in nominal holdings.

The budget constraints represent with the basic identity between sources

and uses of funds for each sector. The presentation here separates current and

2_{For a discussion of accounting principles followed by -.croRconomic and}

financial statistics and their differences see Host-Madsen (1979), particularly

pp. 7-12.

3_{Standards for the preparation of statistics in these four areas have been}

set by United Nations and the International Monetary Fund. A comprehensive guide

for the compilation of no.tional income accounts is United Nations (1968). The

IMF has set the international standards for the three remaining sets of accounts

in its 1948 Balance of Payments Manual (revised subsequently), and in its

periodical publication of the Government Finance Statistics Yearbook and the

capital account sources and uses, defining sector saving as the wabove the line'

or current account excess of sources over uses of funds. This is equal also to

the 'below the line' or capital account ezce s of uses over sources of funds.

Two asset categories are distinguishied ir the capital account: real assets

or physical capital (which has no offsetting liability) and financial assets,

which are claims on another entity. While the changes in physical assets are

written in terms of flows (capital stocks are not considered explicitly in

sections 2.1 - 2.2), changes in financial assets and liabilities are written as

first differences of the corresponding stocks.

A simplifying assumption made throughout the paper, which reflects data

limitations in most applications, is the absence of any current account

transactions of the two financial sectors. This implies that the net wealth or

equity of both the central bank and the banking sector are zero.

To start with, flow budget constraints are written in discrete time4 and

in current prices, i.e., in nominal domestic currency units. Flow variables

refer to the corresponding discrete period (t), while stock variables refer to

end of period (t, or t-l) instants. In order to link subsequently the budget

constraints to real aggregate demand variables, nominal expenditure on these

demand components are separated into the corresponding price and quantum

4_{Discrete-time versions are required for any empirical implementation, as}

flow variables are recorded for discrete time periods, and not as instantaneous

rates. On the other hand, continuous-time models are more convenient for

carrying out steady state and stability analyses due to the higher tractability

of differential equations as compared to difference equations. Additional

drawbacks of discrete-time specifications are first, that the stock-flow

distinction is obscured as shown by May (1970), and second, that they assume a

perfect synchronization of all decisions. For a further discussion of the

differences between discrete and continuous time specifications see Turnovsky

variables. All prices introduced in this subsection, including exchange and

interest rates, are defined as period averages.

Identities (1) and (2) pertain to the central government (G) and public

enterprises and local government (PL), identities (3) and (4) to the central

bank (CB) and the banking sector (BS), identity (5) to the non-financial private

sector (PR), and identity (6) to the foreign sectort

t t PRt Et NTRGOt pCt cGt GTRt GSUBt+ i6t GKTR -+t

7t G t1 3t BGt-l - E it BFGt-l SGt P int +

+ _{(GKTR - GKTRt1 ) + tGKPLt - GKPL t-) Gt Gt-}

- (CBS Gt - CBSGt1) - (BGt - BGtl) Et (BFGt BFGt-l t KTGt

(2) PLFYt + GSUBt - GSUBt - i7t GKPL - i BPLt-1 - Et it BFPLt-1

_ S _ p in - (GKPL -GKPL ) - (B - B ) - (DC _ PLt IT PLt-l t t-l PLt PLt-l PLt CpPLt-1 (CBSPLt PCBSPLt- Et (BFPLt PLt-l (3) 0 5 S CBt (DCGt DCGtl) + (DCPLt - DCPLt1) + (DCBSt DCBSt ) + + Et (RCBt RCBt-l) - (HBSt - HBSt1) (DBBSCBt DBBSCBt-) -(H _PRt -HPRt-1) - (DBPRcBt - DBPRcBt1) - Et ( NCBt - NFBt-) (4) 0 5 S S (CBSGt CBSGt 1) + (CBSPLt_ CBSpLt1) + (HBSt BSt-1)+ + (DBBScBt - DBBSCBt1) _{+ (CBSPRt - CBS Pt-I) + Et (%St}

RSt-- (DCBSt -DCBSt_l) - (DE?PRt - DEPPRt-1) - (Q!Okt - QMONti1)

- Et (NFBBSt - NFBBSt-l)

(5) PRFYt + GTRt + Et NTRPRt + Et WRENt PCt cPRt - TDPRt - Et rrt FKt_j +

i3t BGt-l 8t BPLt-1 Et t RPRt-l 6t KTRt-l t t PRt l

- (DEPPRt - DEPPRtl) + (QMONt - QMONNt-) + ( Gt - BGt-l) ( PLt

-B )PLt-I + Et (RPRt - RPRt l) - (GRTRt - GKTRt_,) - (DPRt - DCPRt l)

- (CBSpRt-₁ - CBSPRt1 ) - Et(FKt - FKt_l) - Et (BPPRt - BFPRt-1)

(6) - Pxt xgnfst + PMINTt mintPRt + PMCt (OCGt + mCPRt ) +

+ I (PRt +miGt + mi ) - E (NTRGO + NTRPR + WREM ) +

+ E rrt FKt + E i (BFGtl + PLtl R+B PR

t t1 t tPLtt-l PRt-1 PRt-1) SFt

E KTGt + Et (FKt - FKt_1) + Et ((BFGt BFGt-l + (BPPLt

_ BFPLt + (BFPRt B PRt-1) + (NCBCBt CNFBCBt ) BSt

- NFBBSt )) - Et((RCBt - RCBt-)) + (RBSt - RBSt- 1) + RPRt - RPRt-l))

where sectors are denoted by the acronyms introduced above and variables are

defined as follows:

FY is gross factor income, TI is indirect taxes, NTR is net foreign

transfers, c is real consumption expenditure, GTR is government transfers to PR,

GSUB is government subsidies to PR channeled via PL, GKTR is government loans

to PR, GKPL is government loans to PL, B is government bonds or domestic debt,

BF is foreign bonds or foreign debt, KTG is foreign capital transfers to the

government, S is saving, in is real gross investment expenditure, DC is domestic

credit of CB, CBS is credit of the BS, R is foreign reserves and asset holdings,

H is base money, DB is deposits at the CB, NFB i.s net foreign debt of financial

institutions, DEP is deposits at BS, QHON is quasi-money held by PR, WREM is

worker remittances from abroad to PR, FK is the foreign-owned capital stock,

xgnfs is real exports of goods and non-factor services, mint is real imports of

intermediate goods, mc is real consumer goods imports, and mi is real capital

Price variables are defined he followss' E is the nominal exchange rate

(which premultiplies all variables defined in nominal foreign currency units),

PC is the consumption deflator, PI is the investment deflator, PX is the domestic

currency deflator for exports, PMINT, PM,, PMC are the domestic currency

deflators for imported intermediate, consumption and investment goods, ij is the

nominal interest rate associated with the jth asset or liability5, i* is the

nominal foreign interest rate, and rr is the nominal rate of profit on

foreign-owned capital.

Equations (1) - (6) are obviously not independent of each other. If one

takes into account the income-( )rnditure identity, any sector's budget equation

is equal to the sum of the other five sectors' budget flow constraints. For

instance, the external sector or balance of payments equation (6) is equal to

the sum of all domestic sectors' budget equations (1) - (5) and the basic

macroeconomic income-expenditure (or national accounts) identity, namely

(7) GFYt + PLFYt + PRFYt + TIt - SUBt ' P Yt - pct (CGt +cPRt) +

PINt(in

-- PHC (mcGt+ mcPRt) - PMIt(miGt+ miPLt + mi PRt

where y is real GDP and P is the GDP deflator.

A compact representation of the interrei.cion between nominal budget

constraints (1) - (7) is given in summary matrix 1, based on Easterly (1989). This presents in a comprehensive format the macroeconomic and financial flows

5_{For notational convenience digits were used for j instead of the}

corresponding to these equetions. The matrix combines the

source-and-use-of-fund presentation and the social accounting matrices consistent with national

income accounts. Each matrix can be divided into four submatrices. The upper

left submatrix represents the current acount transactions, while the two

right-hand submatrices reflect the capital account transactions. The upper-right

submatrix shows investment and the lower-right financial asset transactions.

The lower left submatrix show. the r:aving of each sector as a link between the

current and the capital account transactions. This also allows one to identify

total sector sources and uses of funds. Total domestic saving and investment

are explicitly equated in the lower right-hand corner of the matrix. The

nartional accounts link of GDP to national income and aggregate expenditure is

established in the first row and column of the matrix.

2.2 Flow Budget Constraints in Constant Prices

To derive budget constraints in constant prices, a basic fact to recall

is that a budget constraint in real terms is not linearly independent of the

corrresponding budget constraint in nominal terms, i.e., the former must ba

equal to the latter divided by a common deflator. This paper uses the GDP

deflator for this purpose.

However, after dividing equations (1) - (7) by the average-period GDP

deflator (P), the deflated expenditure on each aggregate demand component is

separated into the real value or quantum component and the relative price change.

On the capital account side, the deflated changes in nominal asset and liability

holdings are separated i!nto the changes in real asset and liability holdings and

For instance, the deflated government consumption expenditure is simply decomposed into constant price or real consumption (equal to consumption

expenditure valued at unit base-period prices) and the relative price change of

consumption goods, versus nationally produced goods as follows:

(8) (PCt cGt) l Pt = cGt +

((Pct

Now let us focus on decomposing the deflated changes in the nominal

holdings of a given asset (or liability) into the sum of the change in real

asset (or liability) holdings and the capital loss (or gain) due to domestic

inflation and exchange rate appreciation. First note that asset and liability

holdings are defined as holdings at end-of-period instants. Therefore

corresponding end-of-period domestic price indices and nominal exchange rates

need to be introduced.6 Defining Pet, Pet_,, Eet, and Eet-, as the relevant

end-of-period domestic price indices and nominal exchange rates, decompose (for

example) for instance the deflated (or average base-period valued) changes in

nominal domestic and foreign government debt holdings as follows:

(9) Gt Gt-l (BFGt -B Gtl

tt

B B

~~p

Gt Gt-l t tl Gtl + t t Gt t

6_{The distinction between period-average and end-of-period deflators,}

introduced here, is not drawn in the six-sector applica.ion of our methodology

etEte EeiE~ 1 tPet Eet

Pet BFGt_,) (1 Ee_, ) Pt BFGt-l (Pr

-ij

t-l t t~~~1

(o bGt-) + (f rt ) b + b +

+ (bfGt bfGt-l) + ( 1 + "it) bfGtl + ( + e2t) bfGt

where lower-case asset holdings denote real holdings valued at end-of-period

prices:

bBG BG- bfEet B

Gt bt Pet Pe1Gt-l Pet Pet₁ bfGt ' P Gt

Eetl1

Gt-l Pe

BFGt-t-l

and 'first-half-term' and *second-half-term, inflation and nominal devaluation

rates are defined as:

lt Pet - Pe t t Pe Pt

fit Pe 'r2t P -P

t-1 Pt

=Et - Ee ti1 Ee -E

t___ _1 _ t t

Domestic government debt accumulation is decomposed in eq. (9) into the

sum of the increase in real (constant) price domestic debt and the government's

capital gain from domestic inflation which erodes the real value of domestic

debt. At the same time, foreign government debt is decomposed by (9) into the

to the real exchange rate appreciation (ir - C > 0) which erodes the real value

(in constant domestic currency prices) of foreign debt.

This decomposition of deflated expenditure flows (as shown by eq. (8)) and

changes in asset and liability holdings (as demonstrated by eq. (9)) is carried

out for every current and capital transaction. Defining the corresponding real

expenditure flows and real financial asset and liability holdings by lower case

letters, tables 1 - 6 present the six flow budget constraints in constant prices

by uses and sources of funds. Again, a distinction is drawn between the current

and capital accounts. Note that in addition to the interest and non-interest

parts of the current account (which comprise the current account of nominal

budget flows), the relative price changes of the corresponding aggregate demand

componerts now appear. In the capital account, the investment relative price

change appears as a new item. Finally, items in the capital account are the

capital gains and losses in real financial wealth stemming from domestic

inflation and nominal eschange rate devaluation.

The interrelations between real budget flows are presented in a compact

form in matr!.x II. It extends the preceding matrix in two dimensions. First,

the national accounts and external sector lines are expanded to consider both

real aggregate demand variables and their price changes relative to the GDP

deflator. Second, deflated changes in asset (liability) holdings in the lower

right submatrix are broken down into changes in real asset (liability) holdings

TABLE 1

SOURCES AND USES OF FUNDS: CENTRAL GOVERNMENT

(In real terms)

ACCOUNTS SOURCES USES

1. Current Account

1.1 Non-Interest GFYt /Pt cGt

TI /Pt _Tt/Pt GTR /Pt_{tl t}

TDPRt/Pt

(Et/Pt ) NTRGOt GSUB t/Pt

1.2 Interest iGt GKTR tIPt i3t BGt-l /Pt

7t G tPL t_1pt (Et/Pt) it BFGt-I

1.3 Consumption Relative (Pc t Pt)/Pt] CGt

Price Change

2. Capital Account

2.1 Investment inGt

2.2 Investment Relative t(PINt - Pt)/P inGt

Price Change

2.3 Capital Grants (Et/Pt ) KTGt

2.4 Real Financial Wealth dcGt - dcGt-1 gktrt gktrt

Changes

cbsGt - CbsGt-l gkplt - gkplt 1

bGt bGt-1

bfGt -bfGt-l

2.5 Real Financial Wealth [lt/( 1

+ it )] (dcGt_l + Erltl/( + rid]

Gains and Losses

cbsGt-l +bGt-l + (gktr t-l+ gkpl t_

TABLE 1 (Contd.)

3_2t

(dcGt + cbuGt + bGt + '2t (gktrt + gkpl )

+ bf )

t( ilt - elt d/1 + fid)] fGt-1[f t- c2dit) + ed

f

62t)/(1

TABLE 2

SOUP.CES AND USES OF FUNDS: PUBLIC ENTERPRISES AND LOCAL GOVERNMENT (In real terms)

ACCOUNTS SOURCES USES

1. Current Account 1.1 Non-Interest PLFY t/Pt 1.2 Interest i7t GKPL t/Pt i8t BPLt-l /Pt (Et/Pt) it BFPLt-l 2. Capital Account 2.1 Investment inPL

2.2 Relative Investment [(PINt- Pt)/Pt]inPLt

Price Change

2.4 Real Financial Wealth

Changes gkplt - gkplt 1

bPLt -bPLt-1

cPLt dcPLt-1

cbsPLt - cbsPLt1

bfPLt - bfPLt-1

2.5 Real Financial Wealth [ritI(l + Iit)

Gains and Losses

(gkplt_ 1 + bPLt-+

+ dcPLt-1 + cbsPLt-l)

r2t (gkplt + bPLt + dc PLt + + cbs PLt)

TABLE 2 (Contd.)

bfp1lt 1

TABLE 3

SOURCES AND USES OF FUNDS: CENTRAL BANK

(In real terms)

ACCOUNTS SOURCES USES

1. Current Account 0 0

2. Capital Account

2.4 Real Financial Wealth hBSt - hBSt-1 dcGt -dcGt-1

Changes dbbscBt - dbbs CBt-l dcPLt - dcPLt-1 hPRt -hpRt-l dcBst - dcBst 1 dbprCBt dbprCBt-l rCBt - rCBt-1 nfb -nfb CBt CBt-i

2.5 Real Financial Wealth r

it/

Gains and Losses

+ dbbsCBt-1 + hPRt-+ (dc Gt-l +

dcPLt-+ dbprCBt- 1) + dcBSt-)

'-2t (hBSt + dbbsCBt 2t (dcGt + dc PLt+

+ hPRt + dbprCB) + dc BS)

[(r It - cid/ (i + irlt)] f(flt - eit)/(l +

ifi+CBt-1l fit lt)I

rCBt-[(f 2t - 2t)/(l + e2td] ('r2t - e2t)I

bCBt-1 (1 + 620]

TABLE 4

SOURCES AND USES OF FUWDS: BANKING SECTOR

(In real terms)

ACCOUNTS SOURCES USES

1. Current Account 0 0

2. Capital Account

2.4 Real Financial Wealth dcBSt - dcBS 1 cbsGt - CbsGt-1

depPRt - dePPRt-1 cbs PLt - cbsPLt-1

qmont - qmont__{1 hBSt - hBSt-1}

nfbSt - nfb BSt- _dbbsCBt - dbbeCBt-1

cbs PRt - cbsPRt-l

rBSt -rBStI

2.5 Real Financial Wealth ['it/(l + 1lt)] (dcBStl +

(rlt

it)

Gains and Losses

+ depPRt-l + qmont-₁ + (cbsGt-l - nfb BSt- + cbs PLt-+ 1_{2t (dcBSt} + dePPRt + +hBSt-l + + qmon t + nfb BS) dbbsCBt-l+ [(T it- Elt)/(l + 1lt) +cbsPRt-l + nfbBSt-l [((T2t (1 +

¶2d]

TABLZ 4 (Contd.) (t Ift - cl)I/( + + Wi) r ₃ id') ' BSt-1 [ (i2t -

e

TABLE 5

SOURCES AND USES OF FUNDS: NON-FINANCIAL PRIVATE SECTOR

(In real terms)

ACCOUNTS SOURCES USES

1. Current Account 1.1 Non-Interest _{PRFYt/Pt cPRt} G t/Pt TDPRt Pt (Et/Pt) NTRPRt (Et/Pt) rrt PKt-1 (Et/Pt) WREMt 1.2 Interest _B6t 1 GKTR /P 3. tPLt-lt _{i /P B}

_~~(E

2.2 Investment Relative [(P P )It]ip

Price Change t t I t

2.4 Real Financial gktr t g ktrt 1 hPRt -hPRt-1

Wealth Changes

dc PRt dc PRt-l dbprcbt - dbprcb t

cbsPRt cbsPRt-1 deppRt -dPPRt-1

fkt - fkti1 qmonl -

qmont-bfPRt - bfPR 1 bGt bGt-1

bPLt -bPLt-I rPRt -rPRtI

TABLE 5 (Contd.)

2.5 Real Financial Wealth [((it/(I + t)] [(I it/(I + 1'

)]

Gains and Losses

(gktr t- + dc Pt-+ (hPRt-I+ + CbSpPRt-1) + dbprcb t1+ + dePPRt- 1 + + qmont 1 + + bGt_l + bPLt-l) f2t (gktrt + dc PRt+ 2t NU + dcprcbt + + cbsPRt) + depPRt + qmont+ G bGt + bPLt)

Iflt -it)I(l + fi-] 1(ylt

Eut)M(

(fkt +bftb _ ₁) + lt ) rPRt-l

[('2t - 62t)/(l + 2t-

)2I)

C2t)/(l

TABLE 6

SOURCES AND USES OF FUNDSs EXTERNAL SECTOR

(In real terms)

ACCOUNTS SOURCES USES

1. Current Account

1.1 Non-Interest

1.1.1 Trade mintPRt + mct + mc PRt+ xgnft

+ miGt + miPLt + MLPRt

1.1.2 Transfers _{(Et/Pt) (NTRGOt +}

+ NTRPKt )

1.1.3 Factor Payments (Et/Pt) rr

t

1.2 Interest _{(EI/P ) i (BFG + (E/P it R...}

+ BPLt-1 + BFPRt-l)

1.3 Export and Import E(PMINTt - Pt)/Pt] mintPRt E(PXt- Pt)/Pt] xgnfat

Relative Price Changes [(PMCt - Pt)/Pt (mcGt+ + MC PRd) [ (PMIt Pt) JPt] (miGt mPLt + PRt) 2. Capital Account

2.3 Capital Grants (Et/Pt) KTG t

2.4 Real Financial r - r fk fk

Wealth Changes CBt CBt-I

f

rPRt - rPRt 1 bfPLt - bfpLt 1

bfpRt - bfPRt-1

nfbcBt - nfbCBt- ₁

TABLE 6 (Contd.)

2.5 Real Financial Wealth

((rlt-

Olt)I(

l

)(flt-

el)/

(l

+

Gains and Losses

(rCBt-1 + rBStl+ (fk t-+bf Gt-+ rPRt-l) bfPLt-l t1 (2t- 2t)/(1 + E2t)] +bfPRt+ (rCBt + rBSt + rPRd) +nfbCBt-l+ nfbBSt-l) E(2t - e2t)I(l + T 62t)] (fkt + + bfGt + bfPLt + + bfPRt + nfb CBt+ + nfbBSt )

Pubi ic

Ent rpri"a Non-Financial

National Central and Loenl Central fanking Private External

Accounts Iovernment orn_nt 8ank Syst Sect ar Sector

(a) (PL) (CS) (OS) (PR) (F)

National ccounte Co CPR E XNFS

- B NCO -E iCpR -E IWPR

Central Governmnt WY _{is Qam}

TI i7 0KPL TDpR E NTROG Public Enterpriccs PLFV and Local Gn_vement 0513 - CSJ8 Central Bank flanking SOyte

Mmn-Financial arR _{E NIAPA}

Privet. Sector _{E Y}

MAFY ia a is 8PL E is RpR

Eaternal Sector E i PF₀ E i*RFpL E rr RC 1

E "Co _E lapR E BFfp E MCPRt SAVIN A bINli Central Covernmnt SC Public Enterpriec and

Local Gover _ent SPL

Central flank Sr8 ' 0

flanking Systee aOS ' 0

Non-Financial

Private Sector SPR

Etemrnal Sector _SF

Total Saving So SPL S ' ° SOS 0 ° SPR SF

Public

Enterprie Non-Financial

Central and Local Central Banking Private External

Government Governmnt Bank Syrte Sector Sector Investment Tot l Source

National Account, Die DIt IR

- E K -E mIpL - SIpR E Subtot. Inv. Y

Central Governmnt Cror Income

Public Enterprises Croes RL Income

and

Loca I Governmnt

Central Banlk Croa" CB Income 0

Banking Syat_m Croe_ BS Income - 0

Non-Financial

Private Sector Cro_m PR Incom

External Sector E NIG E NIpL E I4IpR Imort In. Croe F Income

SAVING A PRROWDIC

E KTC

Central Governmnt dDCO da3Sq dB0 E dSFC C Borrowing * Sawing

Public Enterpriee dPL dDCpL dCBSpL dBpL E dBFp. PL Borrowing * Saving

and

Local Governwent

Central Bank _dDOBSCB fsdP _{n trnl RCB E &*:Am} CS Borrowing * Saving

Banking System dOWPR

dDCgS d*od E dMFDe BS Bbrrowinp * Saving

Non-Financial E dSPpR

Peivate Sector ADR dDCPR dCBSPR E dFK PR Borrowing * Saving

External Sector E dRCS E dRA E dRpFtR F Borrowing * Saving

Total Seving Total Saving

Pub ic

En,terprises Non-F ,ancialI

National Central and Local Central Banking Private External

Accounts Governmnt Governmnt Bank System Sector Sector (0) (Pt) (CO) (U3S) (PR) (F)

National Accounts c "C CPR - (PC(; xgnf* - mintpn C₀ (P'- P)/P cPR (P - P)/P xgnfe (P~ - P)P

eCO (INC - P)/P - cPR (PNC - P)/P m.ntpRj C I4IT - P)/P

Central Governent (GFY * TI)/P i6 GkM/P

P. E. and L. G. (PLFY . GsW)P - CSU0/P Central Bank

Bankiing System

Non-Financial GTR/P (E/P3 T Private Sector *a 8₀/P i₈ BP.jP (E/P) i External Sector (E/P) is 9F0 (E/P) is =pL ,E rr" FKpP

men (~~~~~~~~~~~~~~~~~E/P 1* BFpR mintPR

mCG (PIGl-/P mCPcpR CPNG-P)/P mintpR(PttNr-P)IP

SAVINC A BOPRRMINO 0%

Centrol Covernment SC

Public Enterpri;.c

and

Local Governmnt epL

Central Bank CEt a 0

fanking Systes ot 0 Non-Financial

Private Sector GPR

External Sector *F Total Saving a0 PL aso O * an O am OF

Publ ic

Enterpriiee Non-Finxncial

Central and Local Central Banking Private External

Covorn_nt Government Bank Sy-ta- Sector Sector Investment Total Sources

National Accounts in0 IC inPL - ml* inPR - *NPt y

no JPI - P%SP inpL(Pt -%LrtP inp11 (P P )_p 0

--1PL(P - p)/P ;P ( -P)/P Subtot. Inv.

Central 0a rn.ent Gros Incm

P. E. and L. C Cross PL Incoam

Central Bank Creu- CO Incom. - 0

Banking Sytem Croe b5 Inca. - 0

Non-Financial

Private Sector Cri. PR Incr_w

External Sector *'C *'PL *iPR Cro- F Incme.

faI(PNI - P)/P 1PL (PI, - P)/p *iPR (P"I - P)/P Import Inv.

SAVINOS & BORRING

Central Covernaent ddc0 dcb J dba E/P)KTC dRL C. Bar

dc0 wcba a b0 dbgfQ (.-c)bfC CLL * Svi;ng

Public Enterprias dgkpl ddcpL dcbap1 dbpL dbfpL dRL P1. Bar.

and CUL + Saving

Local Oovernmnt s gkpl * dcpL ff clepi I bpL (i-e)bfpL

Central Bank dbeg aS @ hq; ddPb CBd' nfR Cb('<)nfbdl dRL CO BSr.

Central Sank

~~~~~~~~~~~~~~~~~~~ddhLv

. dm..~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Banking System d.BScs ddeppR ' deppR dnfbaS dRL BS Bar.

* dcg8s dqaon a qmon (r-e)nfb53$ CUL * Saving

Non-Financial dgktr ddcpR dcbe,R dbfpR (if-a)bfPR dRL PR Bar.

Private Sector w gktr ' dcPR * cbapR dfk (z-efk CLL * Saving

drCS dr5s drPR dRL F Bar.

External Sector (C-4)rCe (W-e)re w 'PR CL. * Saving

Total Saving Total

dRA CLA dRA CLA dRA CLA dRA CLA dRA CLA dRA CLA

appreciation.7

2.3 Balance Sheets, Net Wealth and Saving

This section introduces the balance sheets and the corresponding

definitions of net wealth for each sector. Tables 7 - 12 define each sector's

real wealth as the sum of financial wealth (fw) and non-financial wealth.

Non-financial wealth is composed in all but the private sector of non-human wealth

(nhw) or the valued capital stock. In the case of the private sector, a second

component of non-financial wealth is human wealth (hw).

The financial and physical capital variables that comprise net wealth are

consistent with the corresponding flows and stocks which appear in the constant

price budget constraints of tables 1 - 6. However, there is one essential

difference arises between the real flow budget identities in tables 1 - 6 and

the changes in net financial (fwt) and physical (nhwt) wealth consistent with

tables 7 - 12. While constant price budget flows define "under-the-line' saving

(St/Pt) of each sector as the deflated change in nominal financial wealth, the

change in financial and physical wealth (st) subtracts from the former concept

of saving the capital gains (or losses) derived from the erosion in real liabilities (or assets) due to domestic inflation and real exchange rate appreciation:

(10) St ( ft - fwNt-1 ) + (nhw t -nhw _1)

= St /Pt - Capital gains (net of losses) due to inflation and

real exchange rate appreciation in period t.

7 For presentational convenience, all time indices are dropped in both

matrices. Changes in holdings in the lower right submatrices are denoted by the

letter d preceding the corresponding variable name. Capital losses (gains) in

asset (liability) holdings due to inflation or real exchange rate appreciation

Hence the balance-sheet concept (st) equates saving with the net

accumulation of real or constant price wealth. The numerical difference between

this concept of saving and the flow budget measure of saving will be very

substantial in countries with high inflation or significant real exchange rate

depreciation (appreciation).

Capital gains and losses due to high inflation underly the frequent

distinction made between flow public sector dissaving and the public sector

operational deficit, which subtracts from the former the inflation component of

interest payments on indexed domestic public debt8. However, balance sheet

saving in eq. (10) corrects budget flow saving (or distaving) for capital gains

and losses due to inflation and real exchange rate appreciation affecting both

interest and non-interest bearing assets and liabilities.

8_{See World Bank (1988), pp. 56, for a discussion of different measurements}

TABLE 7

BALANCE SHEET: CENTRAL GOVERNMENT

(In real terms, at end of period)

WEALTH COMPONENTS ASSETS LIABILITIES

1. Financial Wealth (fwGt) gktrt dcGt gkplt cbsGt bGt bfGt 2. Non-Financial Wealth 2.1 Non-Human Wealth (nhwGt ) (PKGt/Pt)KGt 3. Net Wealth fwGt

TABLE 8

BALANCE SHEET: PUBLIC ENTERPRISES AND LOCAL GOVERNMENT (In real terms, at end of period)

WEALTH COMPONENTS ASSETS LIABILITIES

1. Financial Wealth (fwPLt) gkplt bPLt dcpLt cbsPLt bfplt 2. Non-Financial Wealth 2.1 Non-Human Wealth 'nhwpLt) (P KPLt /P t) KPLt 3. Net Wealth nwPLt

TABLE 9

BALANCE SHEETs CENTRAL BANK (In real terms, at end of period)

WEALTH COMPONENTS ASSETS LIABILITIES

1. Financial Wealth (fW'CBt) dcGt hBSt dcpLt hPRt dc Bst dbbs CBt rCBt dbbrCBt nfbCBt 2. Non-Financial Wealth 2.1 Non-Human Wealth (nhwCbt) 0 3. Net Wealth nlwCBt = 0

TABLE 10

BALANCE SHEET: BANKING SECTOR (In real terms, at end of period)

WEALTH COMPONENTS ASSETS LIABILITIES

1. Financial Wealth (fwBSt) hBSt dcBst dbbsCBt dePPRt cbsGt qmont cbsPLt nfbBSt cbsPRt rBSt 2. Non-Financial Wealth 2.1 Non-Human Wealth (nhwBSt) 0 3. Net Wealth 3 nwBSt

-TABLE 11

B.ALANCE SHEETs NON-FINANCIAL PRIVATE SECTOR (In real terms, at end of period)

WEALTH COMPONENTS ASSETS LIABILITIES

1. Financial Wealth (fwPRt) hPRt gkt rt bprcbt depRt depRt PcbsPRt qmont fkt bGt bfpRt rPRt 2. Non-Financial Wealth 2.1 Non-Human Wealth (nhwPRt) (P KPRt/P t) KPRt 2.2 Human Wealth hwt 3. Net Wealth nwpRt

TABLE 12

BALANCE SHEET: EXTERNAL SECTOR

(In real terms, at end of period)

WEALTH COMPONENTS ASSETS LIABILTITIES

1. Financial Wealth (FWFt) fkt rCBt bfGt rBSt bfpLt rPRt bfpRt nfbCBt nfbBSt 2. Non-Financial Wealth 2.1 Non-Human Wealth (nhwFt) 0 3. Net Wealth "vFt

2.4 Intertemporal Budget Constraints

The intertemporal budget constraints are the stock or present value

equivalents of the flow budget constraints derived in subsections 2.1. - 2.2.

They can be written as discounted values of either nominal or real expected

future expenditure flows, discounted by the nominal or real interest rate,

respectively. In the following the intertemporal budget equations are written

in real terms, using as deflator the GDP deflator for consistency with the

constant price flow constraints in section 2.2).

Formally, intertemporal budget constraints are derived by forward

integration of expected discounted flow budget constraints, with the added

imposition of a condition that each sector's debt cannot grow systematically at

a rate that exceeds the discount rate (this is known as the no-Ponzi game

condition). The budget constraints simply state that net wealth is equal to the

difference between expected future discounted expenditure and income flows.

In the following the intertemporal budget constraints of only three sectors

are presented: the consolidated public sector, the consolidated

financial/non-financial private sector, and the external sector. Sector consolidation is

ccxsistent with that applied to Zimbabwe in the following section. Variable

definitions are presented in appendix 1.

The intertemporal budget constraints for the public, private, and external

(11) [ h _ ddtt 1 +rPu 1 - fdpTt_i] PhUpUt + +

r

+ Expt [at Rs (ra hs_- + ( + ir ) h81 + r28 h8+

+ ((a. - r ) - (rpU 5 1 fd P s + +

is 15 PUS-! fP )us.8-I)PU~~

+ ( 1 1is r (rPUs-1 fdPUS-i) ( 1 + C (rPus - EdPusM

F

GSUB

TIs

TDppV Ea

1

(

-EXt [st Rs 1 ( Us-

+

(

r

pl+s2

+

[

-

~ ls)

rPPs-l~

fdPS~l)

1 +ezs

)(rPP8

rlls

ftpp))]

(12)

Ih

t

dd

t1+.r p-E

dpp

1,

+

nhwpp_l+Ezpt

tR

+ Expt

Et

+( *- r -rfd )+

1 +

(r

PP

fdpps-1

)

c

(r

Pp -d

I1s

-Expt

Et

Re

cPP

f- + rr, fks-l -

CTPP

I]

+EXPt [sEt

Rs

) c

1P

(13) [ rp_ rpp1 + fdpUt

1

fdpt_P

[

8

8-fk

+ Exp [ sEt Rs 1(i - r) (fdPU81 + fdpp-_l - U8- PP-r +

+ ( 1L isIsr ) (fdiPUs + fd PPs-1 rPUs-1 rPPs-1 )

+ ( 2s) (fdPUS + fdPPs - rPU, - r PP

-ExPt [Et 8 - xgnfs8 + (mintpp + McPUS + Mcpp P +

E

PUS mipp - p (CTPU + CTPP )1 +

+

Exp

Et RRs

xgnfP

) mintpp

+

MCIs. s -P p

+( p8 ) (mcPUS + MPppS) + ( p (miPUS + mippS)I]

where Expt is the expectation conditional on information at the beginning of

period t, r8 is the real discount rate defined as the nominal interest rate paid

on the domestic public debt less the rate of domestic inflation in period s, and

R., the discount factor, is defined as:

R - II 1 r

5 Sint+l 1 +r

The equations distinguish explicitly between the stock components and the expected discounted future flow components of the intertemporal budget

constraints. This is a useful device for differentiating between currently

observed and expected unobserved variables. In addition, on the left-hand side

the equations distinguish between the initial stocks which comprise total

financial and physical (non-human) wealth and the expected future capital

gains/losses due to inflation and real exchange rate appreciation; on the right

hand side; they distinguish between expected future real aggregate demand quantii

and expected future relative price changes affecting those aggregate demand

components.

2.5 Implications of Macroeconomic Consistency for Macro Analysis and Model

Building

The basic feature of the framework developed above is that it assures

consistency, in the sense that budget constraints for the principal sectors of

the economy are all satisfied at the same time. Flow budget constraints form

the basic grid for intratemporal consistency. Flow budget constraints expressed

in real terms allow inter-period comparisons of all relevant variables, and

permit a distinction between real flow variables and their relative price changes

as well as between changes in real asset holdings and capital gains and losses

derived from inflation and nominal devaluation. This provides a useful framework

for carrying out short to medium term financial and macroeconomic programming

for developing economies.

Long-term and solvency questions are addressed by the inter-temporal budget

constraints. These provide the relevant restrictions for ex-ante private sector

In addition, they provide ex-post solvency restrictions for any sector, private

or public, and therefore are essential for carrying out (for instance) an

analysis of the sustainability of public sector deficits.

Budget constraints also impose restrictions on the underlying goods and

asset demands. Asset holdings at any point in time imply what is known as

"adding up" constraints, stressed by Brainard and Tobin (1968) and Tobin (1969).

These state that the sum of the partial derivatives of asset demands with respect

to financial wealth is 1, while the sum of the partial derivatives of asset

demands with respect to any other individual variable (income, asset returns)

is equal to zero.

An analogous adding up constraint holds for the current flow uses of funds

of the private sector: consumption, taxation, and saving. As reflected in any

simple Keynesian model, the sum of the corresponding marginal propensitJes must

be unity. In addition, the sum of the corresponding partial derivatives with

respect to any other variable (interest rates, financial wealth) has to be zero.9

3. APPLICATION TO ZIMBABWE

This section illustrates the usefulness of the consistency framework

developed above by applying it to Zimbabwe. This illustration is a simplified

three-sector version of the six-sector application to Zimbabwe presented in Khadr

and Schmidt-Hebbel (1989).1O

9_{Strictly speaking, the above discussion applies to continuous time. The}

adding up constraints have to be modified slightly for a discrete-time model,

as shown by Turnovsky (1977, pp. 63).

10 For data sources and methodological observations see the paper referred

The three sectors considered here are those of section 2.4 above: the

consolidated public sector (PU) obtained by consolidating the accounts of the

central government, public enterprises and local government, and the central

bank; the financial/non-financial private sector (PP) obtained from a

consolidation of the non-financial private sector and the banking sector; and

the unchanged external sector (F). Definitions of variables and current and

constant flow budget constraints are presented in Appendix 1 of this paper.

3.1 Macroeconomic and Financial Flows in Current Prices

Tables 13-15 depict the current and capital account items in the nominal

budget constraints for the different accounts for the years 1981 and 1987. 1987

was chosen in order to provide the most recent snapshot of resource transfers

in Zimbabwe permitted by data availability. 1981 was chosen as a comparison year

because, as explained below, it exhibits a somewhat different pattern of resource

transfers.

In comparing the structure of nominal flows across the two years, the most

striking difference appears in the way that the excess of public investment over

saving is "absorbed" by an excess of private saving over investment on the one

hand versus foreign saving (i.e., a current account deficit) on the other. In

1981 the excess of public investment over public saving amounted to 13.31Z of

GDP. The corresponding resource transfers were an excess of private saving over

investment (1.4Z) and a current account deficit (11.91Z). In 1987, the picture

is considerably different. The excess of public investment over saving (12.13X

of GDP) is balanced by a much more substantial excess of private saving over

These figures reflect a trend in government policy since the early 1980s

towards controlling external indebtedness through the use of an administered

system of foreign exchange allocation. The latter has increasingly restricted

imports, particularly to the private sector. In turn, the shortage of imports

has repressed investment expenditure and generated *forced" saving. The growing

excess of private saving over investment has fostered an increasing transfer of

resources form the private to the public sector. This has in turn allowed a

persistently large public sector deficit to coexist with a shrinking current

account deficit in the balance of payments. In addition, however, gross domestic

investment has declined from 23.142 of GDP in 1981 to 18.452 in 1987, with most

of the decline explained by lower private sector investment. This decline in

private investment accounts in large measure for the paucity of Zimbabwe's growth

performance since independence.

What are the financial asset changes associated with these resource

transfers? In 1981, the public sector borrowing requirement (PSBR) was 10.6? of

GDP. The lion's share of this (8.232) was financed by external borrowing. In

1987, the PSBR was 12.68Z of GDP. 11.20? of GDP came from domestic debt issues,

with a negligible contribution (0.22? of GDP) from foreign borrowing. For both

years, and particularly 1987, the monetized portion of the PSBR was very small.

This explains how in recent years inflation has been contained in spite of

exceedingly large public sector deficits.

3.2 Macroeconomic and Financial Flows in Constant Prices

Tables 16-18 are the real terms counterparts of Tables 13-15. In terms of

the pattern of resource transfers, the inferences drawn by comparing 1987 with

in the preceding subsection, except that the deflated expenditure components of

GDP can now be split up into a quantity term and a relative price loss term.

For example, in 1981 public investment amounted to 10.952 of GDP. In quantity

(1980 unit base-price) terms, however, it totalled 11.622 of GDP. The -0.67

residualll represents a relative price gain (i.e., a negative loss) attributable

to the fact that the deflator for investment goods or average rose less rapidly

than the GDP deflator between 1980 and 1981. For 1987, the opposite applies.

Public sector investment totalled 10.332 of GDP. In quantity terms, it amounted

to 8.34Z. The 1.992 residual represents the relative price loss that arises from

the fact that the investment deflator on average rose more rapidly than the GDP

deflator between 1980 and 1987.

It is also instructive to examine the decomposition of deflated changes in

holdings of financial assets and liabilities into a change in real stocks12 and

a capital gain/loss component. Consider for example the increase in public sector

domestic debt. In 1981, this amounted to 1.042 of GDP. However, the real debt

burden actually declined by 4.362 of GDP, due to the erosion in the real value

of the outstanding stock of public debt (5.40? of GDP). Even in a relatively low

inflation environment, therefore, 'hidden' transfers to the public sector can

be quite substantial. These transfers are brought out explicitly in the concept

of adjusted saving, which corrects deflated savings for receipts and expenditures

arising from capital gains and losses. As can be seen in the last line of Table

16, adjusted public sector saving (5.222 of GDP in 1981) is markedly different

from (and of opposite sign to) its unadjusted counterpart (-2.36? of GDP).

l1Percentages occasionally do not add up exactly because of rounding errors.

1 2_{Real stocks refer to end-of-period stocks in temss of their end-of-period}

TABLE 13

CONSOLIDATED PUBLIC SECTOR ACCOUNTS (Current Zimbabwe Dollars)

1981 1981(t) 1987 1987(Z) CURRENT SOURCESs

Public Sector Factor Income (PUFY) 161 3.63 650 6.68

Indirect Taxes (TI) A56 10.29 1366 14.05

Direct Taxes Net of Transfers to PP (TDpp) 250 5.64 976 10.04

Current Receipts from F (CTPU) 0 0.00 0 0.00

less CURRENT USES:

Subsidies (SUB) 122 2.75 350 3.60

Public sector Consumption (PC.cpu) 684 15.43 2031 20.89

Interest on Domestic Debt (i.DD) 50 1.13 488 5.02

Interest on Foreign Debt (E.i*.FDpu) 115 2.59 299 3.07

equals PUBLIC SECTOR SAVING (Spu) -104 -2.35 -176 -1.81

equals CAPITAL USES (Asset Accumulation):

Public Investment (PIN.inpu) 486 10.96 1004 10.32

Increase in Foreign Assets (E.dRpu) -120 -2.71 53 0.55

less CAPITAL SOURCES (Liability Accumulation):

Increase in High-powered Money (dH) 44 0.99 3 0.03

Increase in Domestic Debt (dDD) 46 1.04 1089 11.20

Increase in Foreign Debt (E.dFDpu) 365 8.23 21 0.22

Table 14

CONSOLIDATED PRIVATE SECTOR ACCOUNTS (Current Zimbabwe Dollars)

1981 1981(Z) 1987 1987(1)

CURRENT SOURCES &

Private Sector Factor Income (PPFY) 3938 88.83 8058 82.87

Interest Recelved from PU (L.DD) 1.13 488 5.02

Interest on Foreign Assets (E.i*.Rpp) 0 0.00 55 0.57

Current Receipts from F (E.CTPP) -11 -0.25 -37 -0.38

less CURRENT USES:

Private Consumption (PC.cpp) 3046 68.71 5558 57.16

Direct Taxes Net of Transfers from PU (TDpp) 250 5.64 976 10.04

Interest on Foreign Debt (E.i*.FDpp) 0 O.'J0 0 0.00

Profit Remittances to F (E.rr.FK) 79 1.78 98 1.01

equals PRIVATE SAVING (Spp) 602 13.58 1932 19.87

equals CAPITAL USES (Asset Accumulation):

Private Investment (PIN.inpp) 540 12.18 791 8.13

Increase in High-powered Money (dH) 44 0.99 3 0.03

Increase in Domestic Debt (dDD) 46 1.04 1089 11.20

Increase in Foreign Assets (E.dRpp) -5 -0.11 8 0.08

less CAPITAL SOURCES (Liability Accumulation):

Increase in Foreign Debt (E.dFDpp) 37 0.83 -1 -0.01

TABLZ 15

EXTERNAL SZCTOR ACCOUNTS (Current Zimbabwe Dollars)

1981 1961(Z) 1987 1987(Z) CURRENT SOURCESs

Imports of Intermediate Goods (PHINT.mint) 454 10.24 668 6.87

Imports of Consumer goods by PU (PMC.mcpu) 116 2.66 277 2.85

Imports of Consumer Goods by PP (PMC.mcpp) 536 12.09 760 7.82

Imports of Investment Goods by PU (PMI.mipu) 147 3.32 356 3.66

Imports of Investment Goods by PP (PMI.mipp) 165 3.72 280 2.88

Interest Received from PU (E.i*.FDpu) 115 2.59 299 3.07

Interest Received from PP (E.i*.FDpp) 0 0.00 0 0.00

Profit Remittances from PP (E.rr.FK) 79 1.78 96 1.01

less CURRENT USES:

Exports of Goods end Non-factor Services (PX.zgnfs) 1097 24.75 2681 27.57

Transfers to PU (E.CTPU) 0 0.00 0 0.00

Transfers to PP (E.CTPP) -11 -0.25 -37 -0.38

Interest paid to PP (E.i*.Rpp) 0 0.00 55 0.57

equals FOREIGN SAVING (Sf) 526 11.91 39 0.40

equals CAPITAL USES (Asset Accumulation):

Increase in Lending to PU (E.dFDpu) 365 8.23 21 0.22

Increase in Lending to PP (E.dFDpp) 37 0.83 -1 -0.01

Increase in Foreign-held Equity (E.dFK) -14 -0.32 -40 -0.41

Capital Grants to PU (E.KTPU) 15 0.34 120 1.23

less CAPITAL SOURCES (Liability Accumulation):

Increase in Public Foreign Assets (E.dRpu) -120 -2.71 53 0.55

TABLE 16

CONSOLIDATED PUBLIC SECTOR ACCOUNTS (1980 Zimbabve Dollars)

1981 1981(S) 1987 1987(2) CURRENT SOURCES:

Public Sector Factor Income 141 3.63 286 6.69

Indirect Taxes 398 10.28 601 14.05

Direct Taxes Net of Transfers to PP 218 5.64 430 10.04

Current Receipts from F 0 0.00 0 0.00

less CURRENT USES:

Subsidies 107 2.75 154 3.60

Public sector Consumption (cpu) 622 16.06 725 16.94

Interest on Domestic Debt 44 1.13 215 5.02

Interest on Foreign Debt 100 2.59 132 3.08

Public Sector Consumption

Relative Price Change -24 -0.62 169 3.95

equals PUBLIC SECTOR SAVING -91 -2.36 -77 -1.80

equals CAPITAL USES (Asset Accumulation):

Public Investment (inpu) 450 11.62 357 8.34

Increase in PU Foreign Assets -119 -3.08 10 0.24

Public Investment Relative Price Change -26 -0.67 85 1.99

Capital Gain/Loss on PU Foreign Assets 14 0.36 13 0.30

less CAPITAL SOURCES (Liability Accumulation):

Increase in High-povered Money 8 0.20 -16 -0.38

Increase in Domestic Debt -169 -4.36 290 6.78

Increase in PU Foreign Debt 251 6.48 -181 -4.23

Capital Grants from Abroad 13 0.34 52 1.21

Capital Gain/Loss on High-powered Money 30 0.77 17 0.40

Capital GainlLoss on Domestic debt 209 5.40 190 4.44

Capital GainlLoss on PU Foreign Debt 68 1.76 190 4.44

Table 17

CONSOLIDATED PRIVATE SECTOR ACCOUNTS (1980 Zimbabwe Dollars)

1981 1981(Z) 1987 1987(Z) CURRENT SOURCES:

Private Sector Factor Income 3439 88.80 3548 82.88

Interest Received from PU 44 1.13 215 5.02

Interest on Foreign Assets 0 0.00 24 0.57

Current Receipts from F -10 -0.25 -16 -0.38

less CURRENT USES:

Private Consumption (cpp) 2769 71.49 1986 46.39

Direct Taxes Net of Transfers from PU 218 5.64 430 10.04

Interest on Foreign Debt 0 0.00 0 0.00

Profit Remittances to F 69 1.78 43 1.0L

Private consumption Relative Price Change -109 -2.81 461 10.77

equals PRIVATE SAVING 526 13.53 851 19.88

equals CAPITAL USES (Asset Accumulation):

Private Investment (inpp) 500 12.91 282 6.59

Increase in High-powered Money 8 0.21 -16 -0.37

Increase in Domestic Debt -169 -4.36 290 6.77

Increase in PP Foreign Assets -7 -0.17 -20 -0.47

Private Investment Relative Price Change -28 -0.72 66 1.54

Capital Gain/Loss on High-powered Money 30 0.77 17 0.40

Capital Gain/Loss on Domestic Debt 209 5.40 190 4.44

Capital Gain/Loss on PP Foreign Assets 3 0.08 24 0.56

less CAPITAL SOURCES (Liability Accumulation):

Increase in Foreign Debt 22 0.56 -15 -0.35

Increase in Foreign-held Equity -425 -10.96 -331 -7.73

Capital Gain/Loss on Foreign Debt 10 0.26 15 0.35

Capital Gain/Loss on Foreign-held Equity 413 10.66 313 7.31

EXTERNAL SECTOR ACCOUNTS (1980 Zimbabwe Dollars)

1981 1981(Z) 1987 1987(Z) CURRENT SOURCES:

Imports of Intenmediate Goods (mint) 418 10.79 153 3.57

Imports of Consumer Goods by PU (mcpu) 111 2.87 90 2.10

Imports of Consumer Goods by PP (mcpp) 508 13.12 242 5.65

Imports of Investment Goods by PU (mcpu) 137 3.54 147 3.43

Imports of Investment Goods by PP (mcpp) 155 4.00 105 2.45

Interest Received from PU 100 2.59 132 3.08

Interest Received from PP 0 0.00 0 0.00

Profit Remittances from PP 69 1.78 43 1.01

Rel. Price Change on Imports of Intermediate Goods -21 -0.54 141 3.29 Rel. Price Change on Imports of Consumer Goods by PU -8 -0.21 32 0.75 Rel. Price Change on Imports of Consumer Goods by PP -40 -1.03 93 2.17 Rel. Price Change on Imports of Investment Goods by PU -9 -0.23 10 0.23 Rel Price Change on Imports of Investment Goods by PP -11 -0.28 18 0.42 less CURRENT USES:

Exports of Goods and Non-factor Services (xgnfs) 992 25.61 i661 38.80

Transfers to PU 0 0.00 0 0.00

Transfers to PP -10 -0.25 -16 -0.38

Interest paid to PP 0 0.00 24 0.57

Relative Price Change on

Exports of Goods and Non-factor Services -34 ..0.88 -480 -11.21

equals FOREIGN SAVING 461 11.90 17 0.39

equals CAPITAL USES (Asset Accumulation)s

increase in Lending to PU 251 6.48 -181 -4.23

Increase in Lending to PP 22 0.57 -15 -0.35

Increase in Foreign-held Equity -425 -10.97 -331 -7.73

Capital Grants to PU 13 0.34 53 1.23

Capital Gain/loss on Loans to PU 68 1.76 190 4.44

Capital Gain/Loss on Loans to PP 10 0.26 15 0.35

Capital Gain/Loss on Foreign-held Equity 413 10.66 313 7.31

less CAPITAL SOURCES (Liability Accumulation)t

Increase in Public Foreign Assets -119 -3.07 10 0.23

Increase in Private Foreign Reserves -7 -0.18 -20 -0.47

Capital Gain/Loss on Public Foreign Assets 14 0.36 13 0.30

Capital Gain/Loss on Private Foreign Reserves 3 0.08 24 0.56

3.3 Balance Sheets and Real Wealth

Tables 19-21 present briefly stock balance sheets for the three sectors.

As before, all stocks are end-of-period stocks deflated by an end-of-period price

index. Note that the balance sheets have not been explicitly balanced;

constructing a non-financial wealth series is beyond the scope of this study.

The stocks show broad stability, although a marked decline in public

foreign reserves between 1980 and 1981 and an increase in external indebtedness

by the public sector up to 1986 can be noted. Between 1980 and 1987, the real

public debt almost doubled, and foreign-owned equity capital declined steadily,

TABLE 19

BALANCE SHEET: CONSOLIDATED PUBLIC SECTOR

(1980 Zimbabwe Dollars)

WEALTH COMPONENTS ASSETS LIABILITIES

1. Financial Wealth 1980 1981 1986 1987 1980 1981 1986 1987 (fwpu) rPU 136 17 137 147 h 188 196 203 186 dd 1334 1166 2038 2328 fdPU 654 905 2108 1927 2. Non-Financial Wealth 2.1 Non-Human Wealth

(nhwpu ) (PKpu/P) KPU

3. Net Wealth

TABLE 20

BALANCE SHEET: CONSOLIDATED PRIVATE SECTOR (Millions of 1980 Zimbabwe Dollars)

WEALTH COMPONENTS ASSETS LIABILITIES

1. Financial Wealth 1980 1981 1986 1987 1980 1981 1986 1987 (fwpp) h 188 196 203 186 fdpp 101 122 160 145 dd 1334 1166 2038 2328 fk 3948 3523 3470 3140 rpp 21 14 258 239 2. Non-Financial Wealth 2.1 Non-Human Wealth (nhwpp ) (P KPP/P KPP 2.2 Human Wealth hw 3. Net Wealth nw

TABLE 21

BALANCE SHEET: EXTERNAL SECTOR (Millions of Zimbabwe Dollars)

WEALTH COMPONENTS ASSETS LIABILTITIES

1. Financial Wealth 1980 1981 1986 1987 1980 1981 1986 1987 (fwF ) fk 3948 3523 3470 3140 rPU 136 17 137 147 fdPU 654 905 2108 1927 rpp 21 14 258 239 fdpp 101 122 160 145 2. Non-Financial Wealth 2.1 Non-Human Wealth (nhwF ) 0 3. Net Wealth nlWF

4. CONCLUDING REMARKS

This paper has developed a consistency accounting framework for

macroeconomic analysis. The methodology integrates nominal and real, flow and

stock budget constraints in a comprehensive form suitable for application to

countries with reasonably well-developed data bases.

A central feature of the methodology developed here is the inclusion of

constant price flows which permit the introduction of relative prices and real

(quantum) aggregate demand variables as well as capital gains and losses on asset

and liability holdings derived from the effects of inflation and real exchange

rate depreciation.

The application to Zimbabwe shows the potential usefulness of the framework

for carrying out financial programming tasks and serves as an accounting frame

for subsequent model building efforts.

Possible future extensions of the methodology could proceed along the

following lines:

Ci) Inclusion of current account transactions and equity for both the central

bank and the banking sector.

(ii) Disaggregation of the non-financial private sector into firms and

households (which allows explicit treatment of labor and stock market related

variables), and further disaggregation of the latter into wage earners and

non-wage earners (to specify different consumption patterns).

(iii) An explicit link between investment expenditure and physical capital

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Bank, Washington, D. C.

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Khadr, A. and K. Schmidt-Hebbel (1989): A Macroeconomic Consistency Framework

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Constraint and the Crowding-Out Effect." Journal of Monetary Economics,

1, 65-78.

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APPENDIX 1

Three Sector Consolidation of the Consistency Framework

A. Sector Definitions

PU E G + PL + CB PP E PR + BS F E F

B. Definition of Variables PUFY = GFY + PLFY

PPFY = PRFY TDpp = TDPR - GTR CTPU = NTRGO CTPP = NTRPR + WREM DD = B _{BPL + DBPR + DBBS + CBSG + CBSPL -GKTR DCBS} FDPU = BFG + BFPL + NFBCB SPU SG + SPL + SCB

inPU = inG + inPL

inpp = inPR PU= CG cpp = cPR PR BS RPU RCB KTPU = KTG Rpp = RBS + RPR

FD = NFBBS + BFPR Spp = sBS + sPR mcPU = mcG mcpp = mcP mi _Pu mi _G + mi_PL mi = miPR

Note: The interest rates and interest payments have to be redefined according

to the stock redefinitions.

4

C. Flow Budget Constraints in Current Prices

The nominal flow budget constraints for the consolidated public,

consolidated private, and foreign sectors are the following:

(1) PUFY + TIt - GSUDt + TDppt + Et CTPUt P Ct PUt -it t-l

- Et it FDPUt-. = PUt = PINt inPUt (Ht Ht -1 (DDt - DD 1) +

+ Et GRpUt - RpUt_1) - Et (FDPUt - FDPUt_ ) - Et KTPUt

(2) PPFY+Et C t ct cppt TDppt Et rrt FKt 1 + i DD +

t

E i* R t 1 Et it FDppt PPt t t-l t -H

t-1 DDt-l) + Et (R RP Pt_1) - Et (FKIt - FK t _

- Et (FD PPt - FDt-₁ )